Bill de Blasio appointed one of Mayor Bloomberg’s commissioners as his new deputy mayor for health and human services Thursday, and she quickly distanced herself from the administration she’s served for five years.

“I would have done many things differently,” said Lilliam Barrios-Paoli, the commissioner for the aging, when asked about the city’s homeless policy at a press conference announcing her new post.

Specifically, she said she would never have cut funding for homeless prevention — and hinted her objections fell on deaf ears.

“You don’t stop prevention to save money because you end up paying to correct the problem afterwards,” said Barrios-Paoli, who has held numerous positions in city government back to 1980.

“I totally believe we live in a tale of two cities, and it is our job to make it a tale of one city,” she added in a reference to de Blasio’s campaign theme.

Bloomberg has steadfastly rejected the notion that New York is anything but one city.

Before Barrios-Paoli spoke, her boss, Deputy Mayor Linda Gibbs, praised her in a tweet as a “true warrior in the fight against inequality and justice.”

Stu Loeser, Bloomberg’s former press secretary, also weighed in via Twitter and called Barrios-Paoli a “phenomenal pick.”

Homeless advocates criticized the administration in 2011 for ending a program known as Advantage that provided two years of rent subsidies to help people living in shelters find apartments.

The program was scrapped by the city after the state withdrew its share of the funding while grappling with a $10 billion budget deficit. The cut came at a time when homeless shelters were at record levels of occupancy.

Mayor-elect de Blasio said Thursday he would like to restore some type of apartment subsidy.

Barrios-Paoli is considered a safe choice for the new mayor.

She has wide government experience, having served in the Koch and Giuliani administrations before becoming the commissioner of aging in 2008 under Bloomberg.

She also adds diversity to de Blasio’s cabinet as a woman and former Catholic nun who grew up in Mexico.

The mayor-elect’s two earlier appointments, for first deputy mayor and police commissioner, were both white men.

Barrios-Paoli will oversee the city’s health and social-service agencies and has specifically been assigned to expand community health clinics.

“I’ve spent the bulk of my career trying to work on behalf of the poor,” she said at her appointment.

“It is incredibly exciting for me to be in an administration that really makes that a central tenet.”

Barrios-Paoli’s tenure in the Giuliani administration was cut short. She was booted as commissioner of the Human Resources Administration, the city’s sprawling social-services agency, after tangling too often with the former Republican mayor.